WASHINGTON (AP) — President Barack Obama prodded Congress Tuesday to send him a bill by fall remaking the nation's immigration laws, even as the Senate prepared to cast its first floor votes on the landmark measure opening a door to citizenship for millions.

"Congress needs to act, and that moment is now, " Obama said, surrounded by immigration advocates, business and religious leaders, law enforcement officials and others in the East Room of the White House.

"There's no reason Congress can't get this done by the end of the summer," the president said. "There's no good reason to play procedural games or engage in obstruction just to block the best chance we've had in years to address this problem in a way that's fair to middle class families, business owners and legal immigrants."

The Senate was set to vote Tuesday afternoon on a pair of procedural measures to officially allow debate to move forward on the far-reaching legislation. The measure would boost border security and workplace enforcement, allow tens of thousands of new high- and low-skilled workers into the country, and create a 13-year path to citizenship for the 11 million immigrants in the country illegally.

Both votes were expected to succeed by comfortable margins, because even some senators with deep misgivings about the immigration bill said the issue deserved a Senate debate.

Ahead of the votes, senators were readying amendments on contentious issues including border security, back taxes and health care coverage. Some Republicans said they were seeking to strengthen enforcement provisions so that they could be comfortable voting for the bill. Other GOP measures were already being dismissed by Democrats as attempts to kill the bill by striking at the fragile compromises at its core.

Meanwhile House Speaker John Boehner, R-Ohio, made his most positive comments to date on the issue, saying Tuesday he thinks there's a good chance that legislation can be signed into law "by the end of the year."

The way forward in the House remains unclear, because the chamber is dominated by conservatives many of whom view a path to citizenship as amnesty. But Boehner said he hopes for committee action by the end of June.

"I believe that it's important for the House to work its will on this issue," Boehner said on ABC's "Good Morning America." ''And I would expect that a House bill will be to the right of where the Senate is."

"I think, no question, by the end of the year we could have a bill. No question," the speaker said.

As debate opened Tuesday in the Senate, Minority Leader Mitch McConnell, R-Ky., said the bill written by a so-called Gang of Eight — four Republicans and four Democrats — would need stronger provisions on border security and other issues to earn his support.

"The Gang of Eight has done its work. Now it's time for the Gang of 100 to do its work — for the entire Senate to have its say on this issue, and see if we can do something to improve the status quo," McConnell said. "At the risk of stating the obvious, this bill has serious flaws."

Nonetheless McConnell said he intended to vote to allow the debate to go forward. The real fights will come in the days and weeks ahead as Senate Majority Leader Harry Reid, D-Nev., aims to push the bill to final Senate passage before July 4.

The bill's Senate supporters were working to determine which amendments they could accept to lock down more "yes" votes from the GOP side without losing Democratic backing. They are aiming for a resounding show of support from the Democratic-led Senate that could pressure the House to act.

Heated debate is anticipated on the border security elements of the bill. The bill sets up a system wherein immigrants may only begin taking steps toward citizenship once certain border security requirements are met. But opponents say those "triggers" aren't strong enough.

An amendment announced by Sen. John Cornyn, R-Texas., would require 100 percent monitoring of the entire U.S.-Mexico border and 90 percent of would-be crossers to be stopped or turned back before anyone can get a permanent resident green card. The Senate bill, authored by a bipartisan group of eight senators, also sets those figures as goals, but doesn't make the path to citizenship directly contingent on them.

"My amendment demands results while the Gang of Eight bill is satisfied with just more promises, promises that historically have never been kept," Cornyn said Tuesday on the Senate floor.

But in an interview over the weekend with Univision, Reid dismissed Cornyn's amendment as a "poison pill."

"If people have suggestions like they did in the Judiciary Committee to change the bill a little bit, I'll be happy to take a look at that," Reid said. "But we're not going to have big changes in this legislation."

It's not likely to be Cornyn's, but supporters of the bill were looking for a border security measure they could support. It could be an amendment pushed by Sen. Marco Rubio, R-Fla., an author of the bill who's talked about giving Congress a more direct role in developing a border security plan that the bill now leaves to the Homeland Security Department.

"One of the objections we've heard from the opponents of the bill is 'we don't trust Homeland Security to come up with a plan that works.' Fine. Then let's put it in the bill," Rubio said Tuesday. "Let's put the specific plan in the bill, the number of fences, the amount of technology. Let's mandate it in the bill so that we're not leaving it to guesswork, so that when you vote for this bill you are voting for a specific security plan."

Other disputes will surround amendments being pushed by Sen. Orrin Hatch, R-Utah, to strengthen requirements for payment of back taxes in the bill and require previously illegal immigrants who get green cards under the bill to wait five years before beginning to access benefits under the nation's new health care law.